Concept
Snub (geometry)
Related concepts (20)
Snub disphenoid
In geometry, the snub disphenoid, Siamese dodecahedron, triangular dodecahedron, trigonal dodecahedron, or dodecadeltahedron is a convex polyhedron with twelve equilateral triangles as its faces. It is not a regular polyhedron because some vertices have four faces and others have five. It is a dodecahedron, one of the eight deltahedra (convex polyhedra with equilateral triangle faces), and is the 84th Johnson solid (non-uniform convex polyhedra with regular faces).
Snub square antiprism
In geometry, the snub square antiprism is one of the Johnson solids (J_85). It is one of the elementary Johnson solids that do not arise from "cut and paste" manipulations of the Platonic and Archimedean solids, although it is a relative of the icosahedron that has fourfold symmetry instead of threefold. The snub square antiprism is constructed as its name suggests, a square antiprism which is snubbed, and represented as ss{2,8}, with s{2,8} as a square antiprism. It can be constructed in Conway polyhedron notation as sY4 (snub square pyramid).
Uniform tilings in hyperbolic plane
In hyperbolic geometry, a uniform hyperbolic tiling (or regular, quasiregular or semiregular hyperbolic tiling) is an edge-to-edge filling of the hyperbolic plane which has regular polygons as faces and is vertex-transitive (transitive on its vertices, isogonal, i.e. there is an isometry mapping any vertex onto any other). It follows that all vertices are congruent, and the tiling has a high degree of rotational and translational symmetry.
Snub polyhedron
In geometry, a snub polyhedron is a polyhedron obtained by performing a snub operation: alternating a corresponding omnitruncated or truncated polyhedron, depending on the definition. Some, but not all, authors include antiprisms as snub polyhedra, as they are obtained by this construction from a degenerate "polyhedron" with only two faces (a dihedron). Chiral snub polyhedra do not always have reflection symmetry and hence sometimes have two enantiomorphous (left- and right-handed) forms which are reflections of each other.
Great retrosnub icosidodecahedron
In geometry, the great retrosnub icosidodecahedron or great inverted retrosnub icosidodecahedron is a nonconvex uniform polyhedron, indexed as U_74. It has 92 faces (80 triangles and 12 pentagrams), 150 edges, and 60 vertices. It is given a Schläfli symbol sr{,}.
Square antiprism
In geometry, the square antiprism is the second in an infinite family of antiprisms formed by an even-numbered sequence of triangle sides closed by two polygon caps. It is also known as an anticube. If all its faces are regular, it is a semiregular polyhedron or uniform polyhedron. A nonuniform D4-symmetric variant is the cell of the noble square antiprismatic 72-cell. When eight points are distributed on the surface of a sphere with the aim of maximising the distance between them in some sense, the resulting shape corresponds to a square antiprism rather than a cube.
Great inverted snub icosidodecahedron
In geometry, the great inverted snub icosidodecahedron (or great vertisnub icosidodecahedron) is a uniform star polyhedron, indexed as U69. It is given a Schläfli symbol sr{,3}, and Coxeter-Dynkin diagram . In the book Polyhedron Models by Magnus Wenninger, the polyhedron is misnamed great snub icosidodecahedron, and vice versa.
Regular icosahedron
In geometry, a regular icosahedron (ˌaɪkɒsəˈhiːdrən,-kə-,-koʊ- or aɪˌkɒsəˈhiːdrən) is a convex polyhedron with 20 faces, 30 edges and 12 vertices. It is one of the five Platonic solids, and the one with the most faces. It has five equilateral triangular faces meeting at each vertex. It is represented by its Schläfli symbol {3,5}, or sometimes by its vertex figure as 3.3.3.3.3 or 35. It is the dual of the regular dodecahedron, which is represented by {5,3}, having three pentagonal faces around each vertex.
Snub 24-cell
In geometry, the snub 24-cell or snub disicositetrachoron is a convex uniform 4-polytope composed of 120 regular tetrahedral and 24 icosahedral cells. Five tetrahedra and three icosahedra meet at each vertex. In total it has 480 triangular faces, 432 edges, and 96 vertices. One can build it from the 600-cell by diminishing a select subset of icosahedral pyramids and leaving only their icosahedral bases, thereby removing 480 tetrahedra and replacing them with 24 icosahedra.
Snub square tiling
In geometry, the snub square tiling is a semiregular tiling of the Euclidean plane. There are three triangles and two squares on each vertex. Its Schläfli symbol is s{4,4}. Conway calls it a snub quadrille, constructed by a snub operation applied to a square tiling (quadrille). There are 3 regular and 8 semiregular tilings in the plane. There are two distinct uniform colorings of a snub square tiling. (Naming the colors by indices around a vertex (3.3.4.3.4): 11212, 11213.